Finite Group DatabasebetaFinite Group Databasebeta| order | 29110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C41×C71 ⋊ C2×C5 |
| Hall | #28410025 ⋊ C2 |
| Hall | D2911 ⋊ C5 |
| Sylow | C71 ⋊ D41⋊C5 |
| Sylow | C41 ⋊ D71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C71 | C2×C5 |
| LCS | G ▷ C41×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2911 |
Polycyclic presentation:
2,5,41,71|c^a=c^40,d^a=d^70,c^b=c^10,d^b=d^25301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29110, 32);